Source-linked AI summary
Optimal network modularity for information diffusion
Azadeh Nematzadeh, Emilio Ferrara, Alessandro Flammini, Yong-Yeol Ahn
TL;DR
The paper asks how community structure and social reinforcement jointly affect global information diffusion. Using the linear threshold model with analytical and numerical approaches, it finds an optimal modularity that minimizes the early adopters required for global diffusion.
Problem
The paper addresses limited systematic understanding of how social reinforcement interacts with modular community structure in information diffusion.
Method
The study uses the linear threshold model, analytical approaches, numerical simulations, and network ensembles with varying community structure.
Results
An optimal community strength facilitates global diffusion by enhancing local spreading while retaining sufficient inter-community connectivity; specifically, µc ≃0.2175 requires the minimal seeds compatible with global diffusion.
Takeaways & Limitations
The right amount of modularity can counterintuitively enhance global information diffusion rather than hinder it.
Takeaways & Limitations
The presented main results focus on random networks with two communities and a specific threshold value, although supplementary evidence broadens this scope.
Abstract
from arXiv · showhide
We investigate the impact of community structure on information diffusion with the linear threshold model. Our results demonstrate that modular structure may have counter-intuitive effects on information diffusion when social reinforcement is present. We show that strong communities can facilitate global diffusion by enhancing local, intra-community spreading. Using both analytic approaches and numerical simulations, we demonstrate the existence of an optimal network modularity, where global diffusion require the minimal number of early adopters.
Introduction
Using analytical approaches and numerical simulations, the study examines information diffusion under varying network configurations and identifies an optimal modularity requiring minimal early adopters.
- The study models diffusion with the linear threshold model and initializes a fraction ρ0 of randomly selected agents as seeds in one community.
- Analytical approaches and numerical simulations demonstrate a nontrivial optimal modularity where global cascades require the minimal number of early adopters.
- The supplementary analysis varies θ, average degree z, network size N, number of communities, degree distribution, and community size distribution.
Average degree and clustering coefficient
Changing average degree and clustering preserves the qualitative diffusion behavior, while higher average degree shifts the optimal mixing parameter upward.
- Increasing average degree does not change the qualitative behavior of the diffusion dynamics.
- As average degree increases, the optimal value of µ also increases.
- Strong clustering hardly changes the qualitative behavior of the system.For µ = 0.23, the clustering coefficient is 0.226; for µ = 0.01, it is 0.38.
Disassortative (bipartite) mixing
Across the full mixing range, global cascades arise through distinct regimes, while the optimal mixing parameter remains near 0.25 despite changing minimum seed requirements.
- The minimum ρ0 for a global cascade increases until around µ = 0.45 and decreases thereafter.
- The optimal mixing parameter remains around 0.25 across the examined µ range.
- For large µ, adoption alternates longitudinally between communities rather than developing first in the originating community and then spreading to the second.
- The phase diagram distinguishes assortative modular mixing for µ < 0.5, random mixing at µ = 0.5, and disassortative bipartite mixing for µ > 0.5.
Network size
Simulations indicate that network size does not affect the reported diffusion results.
- The size of networks does not affect the results.
Number of communities
The optimal-modularity behavior persists beyond two communities, including in more realistic LFR networks, but increasing community count lowers the adoption threshold needed for complete cascades.
- The optimal-modularity behavior persists when the number of communities exceeds two.
- The same qualitative behavior appears in LFR networks with heterogeneous degree and community-size distributions.LFR networks are described as more realistic than networks with uniform structural properties.
- More communities require a smaller adoption threshold to complete the cascade.The passage attributes this to fewer bridges among communities as community count increases.
Adoption threshold
Across a broad range of adoption thresholds, the model shows qualitatively similar behavior, but thresholds above 0.5 produce a qualitative change in how modularity affects global cascades.
- Qualitatively similar behavior persists across threshold values up to approximately θ = 0.5.The result is reported for both TL approximation and simulation phase diagrams.
- When θ > 0.5, the behavior changes qualitatively.
- At very large thresholds, higher µ allows the global cascade to occur earlier.